Help Your Students Better Understand Fractions with Different Denominators

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In the world of fractions, numbers seem to have a split personality. You know, they get to represent part of something while also representing a number in an operation. It’s no wonder that children find them so confusing. But, once they get to know them, their properties, and how they work, they actually can be very useful tools in math. So how can we help students better understand fractions, especially when they have to add and subtract fractions with different denominators? Let’s tackle that so we can throw this tool into our toolbox!

Use Visuals for Understanding

Number lines are a great visual to help students understand exactly what is happening when they are adding and subtracting fractions with different denominators. Then students are not just going through the motions of changing the numbers but not understanding why they changed them. You will be amazed at how many children changed the numbers and added them but couldn’t tell you why. Draw a number line on the board and demonstrate for students adding or subtracting another fraction. After you have done this a few times, have your students try it.

Fun Activity with this method: Fraction Hopscotch

Break students up into groups and have them create a large number line on the ground using sentence strips and index cards. Provide each student with a token and have them start at zero. Provide the starting student with a die that has fractions on it. You can purchase them online or create your own using wooden blocks. The starting student will roll the die and read the fraction aloud. Then they move their token to that place on the number line. The next player will roll the die and move their token to that place on the number line. The play continues like this with students adding their rolled fraction to their place on the number line. If a player cannot add their fraction with the previous fraction, they must subtract it. The game continues until a player reaches the end of the number line first.

Use Manipulatives for Teaching

When students can physically manipulate objects it helps make the concepts more concrete for them. Consider providing fraction bars, cubes, or tiles so that they can visualize and understand adding and subtracting fractions with different denominators. This also moves them one step closer to creating common denominators on paper. We are working our way up to a more abstract level! It won’t be long now!

Fun Activity with this method: Fraction Pizza

Break students up into groups of 4 to 5 students and provide them with fraction circle manipulatives, construction paper in the shape of a large circle, glue, and scissors. Have students divide their paper circles into equal slices to represent their fraction circle manipulatives and name them. Next, have the students trade slices with different people in their group. Now they will add or subtract these slices to their slices. Have the students glue their new slices with their slices, making sure they fit together like puzzle pieces. Have students repeat the process until their entire pizza is complete. If desired, you can have them color their pizza slices that now have fractions with different denominators.

Use Equivalent Fractions to Create Common Denominators

Before you can run, you have to walk. It’s the same with adding and subtracting fractions with different denominators. If students cannot find equivalent fractions then they won’t be able to add or subtract any fractions with different denominators. It’s just the way it is. I’d pull a seat up next to them and just mini-assess. Can they find an equivalent fraction? Do they know what the lowest common denominator is? If they can’t with those two, start there! You can find a few ideas on my engaging ways to teach equivalent fractions post to help you review those concepts and get some much-needed practice in. Once you are sure students know how to find a common denominator, teach them how to rewrite the fractions using equivalent denominators and create equivalent fractions. Then they are good to go with just adding or subtracting the fractions.

Fun Activity with this method: Fraction Caterpillar

Provide students with colorful circle cut-outs (use your school die-cut machine). How many is up to you, but enough to represent a caterpillar’s head and body segments. (Alternatively, you can draw circles on a piece of paper and write fractions in each circle. Then make copies). When you provide students with the circle cut-outs, also tell them what fractions to write into the circles or you can write it into the circles yourself. I would assign each color a fraction and write a “key” on the board. Next, have students find a common denominator for all their segments and add or subtract the fractions on their caterpillar to find the total.

Extra Practice to Reinforce

Once students have the concepts down, you can then move them into the abstract level and provide them with plenty of opportunities to practice so that it is reinforced. We want students to remember how to add and subtract fractions with different denominators in the future and the best way to do that is to provide plenty of practice.

Fun Activity with this method: Fraction War

Provide students with a deck of fraction cards that are created or purchased. Have students partner up and each takes a stack of fraction cards. They play by flipping two cards at the same time and adding or subtracting the fractions with different denominators to find the result. The player who has the largest sum or difference wins both sets of cards for that round. The play continues in this manner until one player has all the cards.

With these activities that move from concrete to more abstract, students are sure to better learn and understand adding and subtracting fractions with different denominators. Additionally, these activities will help them be engaged and enjoy it a little too!